Can someone point me in the direction of the algorithms that I should study in order to solve the following problem:
I have about 10 variables. They are constantly changing, I record their changes. I need to find different places in the data where the movement of the variables is the same: in both places x1 increases by 50%, x2 falls by 20%, x3 remains in place, etc. For all 10. Say that this happens on time at point 15 and again at time 225. I need to recognize this scheme, so I need to create a “signature” for each general category of such a sum of movements.
Optimally, this signature should apply to fairly long lines: x1 up 15%, down 20%, up 30%, but always for all 10 variables together. In financing, they probably should do this for stock analysis, but what algorithms do they use?
EDIT: I look at multidimensional trees in the first answer, but now I also look at an alternative way: since the values should be up to a hundred, and I can come closer to higher values (something over 50% evaluates to “more than half”, for example) , then I can use the fact that the higher "shelves" can be occupied only by a very limited number of variables (only one "more than half", only 3 in the category "30-50%", etc.) to reduce the overall the amount of possible changes for each recorded distribution. I could build a hash function to give a key for each distribution, and then include with it the keys for each distribution that follow the original distribution.
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